The linear velocity of a rotating body is given by v=ω×r, where ω is the angular velocity and r is the radius vector. The angular velocity of a body, ω=i^-2j^+2k^ and their radius vector is  r=4j^-3k^, then value of |v| will be:

1.  29 units

2.  31 units

3.  37 units

4.  41 units

Subtopic:  Vector Product |
 76%
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The displacement of a particle is given by y=a+bt+ct2-dt4. The initial velocity and initial acceleration, respectively, are: (\(Given: v=\frac{dx}{dt}~and~a=\frac{d^2x}{dt^2}\))

1.  b, -4d

2.  -d, 2c

3.  b, 2c

4.  2c, -4d

Subtopic:  Differentiation |
 77%
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The momentum is given by p=4t+1, the force at t=2s is-[Given: F=dPdt]

(A)  4 N

(B)  8 N

(C)  10 N

(D)  15 N

Subtopic:  Newton's Laws |
 79%
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If the momentum of a particle is given by P=(180-8t) kg m/s, then its force will be-[Given: F=dPdt]

(1)  Zero

(2)  8 N

(3)  -8 N

(4)  4 N

Subtopic:  Newton's Laws |
 83%
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The maximum value of the function 7+6x-9x2 is:

1.  8

2.  -8

3.  4

4.  -4

Subtopic:  Differentiation |
 66%
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If fx=x2-2x+4, then f(x) has:

1.  a minimum at x=1.

2.  a maximum at x=1.

3.  no extreme point.

4.  no minimum.

Subtopic:  Differentiation |
 66%
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A particle is moving along x-axis. The velocity v of particle varies with its position x as v=1x. Find velocity of particle as a function of time t given that at t=0, x=1 .

1.  v=2t+1

2.  v=12t+1

3.  v=1t

4.  None of these

Subtopic:  Integration |
 60%
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A vector A is directed along 30° west of north direction and another vector B along 15° south of east. Their resultant cannot be in ____________ direction.

(1)  North

(2)  East

(3)  North-East

(4)  South

Subtopic:  Resultant of Vectors |
 58%
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ABCD is a quadrilateral. Forces BA, BC, CD & DA act at a point. Their resultant is 

(A)  2 AB

(B)  2 DA

(C)  zero vector

(D)  2 BA

Subtopic:  Resultant of Vectors |
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The maximum and minimum magnitude of the resultant of two vectors are 17 units and 7 units respectively. Then the magnitude of resultant of the vectors when they act perpendicular to each other is:

(1)  14

(2)  16

(3)  18

(4)  13

Subtopic:  Resultant of Vectors |
 68%
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